{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:R5MSFZVVXUJ4S7D7OENVD4L4JA","short_pith_number":"pith:R5MSFZVV","schema_version":"1.0","canonical_sha256":"8f5922e6b5bd13c97c7f711b51f17c481fc6fc7635f76dc5647d4c661ee5eca9","source":{"kind":"arxiv","id":"2508.08102","version":1},"attestation_state":"computed","paper":{"title":"Knot primality: knot Floer homology, metacyclic representations and twisted homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Charles Livingston, Samantha Allen","submitted_at":"2025-08-11T15:40:51Z","abstract_excerpt":"We develop purely algebraic methods for proving that a knot is prime. Our approach uses the Heegaard Floer polynomial in conjunction with classical knot-theoretic methods: cyclic, dihedral, and metacyclic covering spaces. The theory of twisted homology allows us to view these approaches from a unified perspective. Collectively, the primality tests developed here have proved primality for over 99.6% of knots in large families of prime knots, including all prime knots with 15 or fewer crossings."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2508.08102","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2025-08-11T15:40:51Z","cross_cats_sorted":[],"title_canon_sha256":"9930a489bef889e6468293a69af0ed4f89778e0548d2358b49397f8848859097","abstract_canon_sha256":"076e88fef7a445716d36fa1d735fa6615daf99cfa36b903c3c42bbd85b4331b1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:52:08.270812Z","signature_b64":"JDaxANRTmS7Pg7Moi1+pcWwoPHqUpbAvL/sLOLRFWq7gkgX+pZoj6y8i4GYSyklCBAWBJYc48VCRgwrVqAZSCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8f5922e6b5bd13c97c7f711b51f17c481fc6fc7635f76dc5647d4c661ee5eca9","last_reissued_at":"2026-07-05T11:52:08.270399Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:52:08.270399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Knot primality: knot Floer homology, metacyclic representations and twisted homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Charles Livingston, Samantha Allen","submitted_at":"2025-08-11T15:40:51Z","abstract_excerpt":"We develop purely algebraic methods for proving that a knot is prime. Our approach uses the Heegaard Floer polynomial in conjunction with classical knot-theoretic methods: cyclic, dihedral, and metacyclic covering spaces. The theory of twisted homology allows us to view these approaches from a unified perspective. Collectively, the primality tests developed here have proved primality for over 99.6% of knots in large families of prime knots, including all prime knots with 15 or fewer crossings."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.08102","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2508.08102/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"2508.08102","created_at":"2026-07-05T11:52:08.270455+00:00"},{"alias_kind":"arxiv_version","alias_value":"2508.08102v1","created_at":"2026-07-05T11:52:08.270455+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2508.08102","created_at":"2026-07-05T11:52:08.270455+00:00"},{"alias_kind":"pith_short_12","alias_value":"R5MSFZVVXUJ4","created_at":"2026-07-05T11:52:08.270455+00:00"},{"alias_kind":"pith_short_16","alias_value":"R5MSFZVVXUJ4S7D7","created_at":"2026-07-05T11:52:08.270455+00:00"},{"alias_kind":"pith_short_8","alias_value":"R5MSFZVV","created_at":"2026-07-05T11:52:08.270455+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/R5MSFZVVXUJ4S7D7OENVD4L4JA","json":"https://pith.science/pith/R5MSFZVVXUJ4S7D7OENVD4L4JA.json","graph_json":"https://pith.science/api/pith-number/R5MSFZVVXUJ4S7D7OENVD4L4JA/graph.json","events_json":"https://pith.science/api/pith-number/R5MSFZVVXUJ4S7D7OENVD4L4JA/events.json","paper":"https://pith.science/paper/R5MSFZVV"},"agent_actions":{"view_html":"https://pith.science/pith/R5MSFZVVXUJ4S7D7OENVD4L4JA","download_json":"https://pith.science/pith/R5MSFZVVXUJ4S7D7OENVD4L4JA.json","view_paper":"https://pith.science/paper/R5MSFZVV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2508.08102&json=true","fetch_graph":"https://pith.science/api/pith-number/R5MSFZVVXUJ4S7D7OENVD4L4JA/graph.json","fetch_events":"https://pith.science/api/pith-number/R5MSFZVVXUJ4S7D7OENVD4L4JA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R5MSFZVVXUJ4S7D7OENVD4L4JA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R5MSFZVVXUJ4S7D7OENVD4L4JA/action/storage_attestation","attest_author":"https://pith.science/pith/R5MSFZVVXUJ4S7D7OENVD4L4JA/action/author_attestation","sign_citation":"https://pith.science/pith/R5MSFZVVXUJ4S7D7OENVD4L4JA/action/citation_signature","submit_replication":"https://pith.science/pith/R5MSFZVVXUJ4S7D7OENVD4L4JA/action/replication_record"}},"created_at":"2026-07-05T11:52:08.270455+00:00","updated_at":"2026-07-05T11:52:08.270455+00:00"}